This functor takes a collection of graded algebras (possibly with
basis) and constructs the signed tensor product of those algebras.
If this algebra is in a subcategory, say that of
Algebras(QQ).Graded(), it is automatically endowed with
its natural algebra structure, thanks to the category
Algebras(QQ).Graded().SignedTensorProducts() of signed tensor
products of graded algebras.

The signed tensor functor is covariant: if A is a subcategory
of B, then A.SignedTensorProducts() is a subcategory of
B.SignedTensorProducts() (see also
CovariantFunctorialConstruction). Hence,
the role of Algebras(QQ).Graded().SignedTensorProducts() is solely
to provide mathematical information and algorithms which are relevant to
signed tensor product of graded algebras.

Those are implemented in the nested class
SignedTensorProducts
of Algebras(QQ).Graded(). This nested class is itself a subclass of
SignedTensorProductsCategory.